1. Field of the Invention
The present invention relates to a two dimensional digital micro-mirror, more specifically, to a multi-step landing micro-mirror, a method for manufacturing the same, and a multi-step landing micro-mirror array.
2. Description of the Prior Art
In an optical switch using a micro-mirror, various forces such as an electrostatic force, an electromagnetic force, a thermal expansion force, and a self stress force of a material are applied depending on the driving methods. Among them, the driving method using the electrostatic force has convenience of the manufacturing process, a low power consumption, tolerance for an external noise, compared with a different kind of actuation method. As the micro-mirror using the electrostatic force, the mirror attached with a torsion beam by a spring is commonly used. This uses a principle that a displacement angle is variable in proportional to an applied voltage.
The conventional torsion mirror type actuation method using the electrostatic force can be divided into the next two application examples. First, the three dimension micro-mirror precisely implements the rotation angle obtained when the strength of the electrostatic force is equal to that of the restoring force of the spring. On the other hand, the two dimensional micro-mirror is a state of switching off when the rotation angle is 0 degree, and when the rotation angle is 90 degree, it arranges the digital mirrors in a m×m (m=1,2,3, . . . , m) matrix shape. The spring, mechanically supporting the digital mirror should be sufficiently weak in order to increase a switching speed. However, the spring is sufficiently strong in order to increase the speed for restoring the mirror to the original location thereof due to the restoring force. Accordingly, the spring must be designed to have the optimal state under this trade-off relationship. In addition, the mirror must be designed strongly not to generate a translation displacement. The translation displacement means that the central axis is changed in generating the displacement angle. The material and the dimension of the spring, and the voltage applied to the mirror must be determined to satisfy the trade-off requirement.
Hereinafter, the problems of the conventional digital mirror will be explained with reference to FIGS. 1A and 1B.
FIGS. 1A and 1B illustrate a conventional digital mirror, wherein FIG. 1A is a perspective view of the digital mirror and FIG. 1B is a cross sectional view of the digital mirror. Referring to FIGS. 1A and 1B, a digital mirror comprises a plate 10, a mirror 11, a torsion spring 12, and a trench 13. In the digital mirror, one torsion spring is attached to each of the both ends of the mirror, and the torsion spring is subjected to the torsion stress of 90 degree even at the state of switching-on. At this time, the displacement angle θ for driving of the mirror is determined in the point that the electrostatic force due to the voltage is equal to the restoring force of the spring. The spring must be designed such that the mirror is rotated by 90 degree by the electrostatic force at the switching-on state and the mirror has a sufficient restoring force and a fast switching speed in the switching-off state. The electrostatic force is determined by the distance between an electrode applied to a voltage and the mirror size, when the size of the micro-mirror is determined. In addition, the restoring force is determined by a spring constant such as the material, the width, the thickness, and the length of the spring and the shape of the spring.
The cases that the rotation angle for driving the conventional digital mirror is 90 degree and 30 degree will be explained in comparison to each other.
The electrical torque Telec. for generating the displacement of the mirror is express by the next equation 1.Telec.=(½)eoWV2∫x/[(d/sin θ−x)θ]2dx
Further, the mechanical torque Tmech. of the spring is expressed by the next equation 2.Tmech.=2(Gwt3(1−(192t/x5w)tan h(.πw/2t)))θ
Accordingly, if the needed rotation angle is large, the electrical torque becomes also large, so that the applied voltage must be large. In addition, in order to decrease the applied voltage, among the dimensions of the spring, the width w of the spring must be decreased, the length (l) thereof must be increased, or the thickness (t) thereof must be decreased. In Particular, since the mechanical torque Tmech. in the equation 2 is proportional to the third power (t3) of the thickness of the spring, the needed force can be decreased to 1/√27, by decreasing the thickness of the spring to ⅓. Therefore, the voltage can be decreased to 1/√27. However, if the thickness of the spring is ⅓, there is a problem that the central axis of the mirror is moved because of weaken mechanical support. Also, there could be a problem that the speed of the switch-off due to the decrease of the restoring force at the switching-off state is decreased.
The torsion spring 12 must endure the torsion stress by 90 degree, and it is very difficult that the central axis of the mirror is intended not to move even at such stress state. In addition, the large voltage is needed in order to rotate the mirror by 90 degree, so that there are the difficulty of the driving and the possibility of the arc plasma between mirror and trench when mirror is on state. The fatigue phenomenon of the spring due to the torsion stress by 90 degree affects the reliability.